Hi, welcome to the forum :drink:
As Mark says, you can put the lid on tightly if you have an airlock, if you don't have an airlock just leave space for the gas to escape.
During fermentation a lot of CO2 is produced and this needs to be able to escape otherwise the pressure will build up in the bucket.
You should test the gravity of the wort with the hydrometer before you pitch the yeast, this will tell you the amount of sugar there is in the wort that could potentially become alcohol. You would be looking for something in the region of 1040.
You should also use the hydrometer to test if fermentation has finished, usually after 7 to 10 days, the reading should be closes to 1012, if it stays constant like that then you are fine to put into bottles.
I can't see any reason to test the gravity of the wort in the middle of fermentation as Mark suggests, I can't see what this would tell you.
The pressure barrel is where you put the beer to dispense it from. Once fermentation has finished you would transfer the wort to the pressure barrel, adding some sugar. The sugar then undergoes some fermentation in the barrel, producing CO2, which creates pressure in the barrel and carbonates the beer slightly. I say slightly as pressure barrels can only really hold about 10psi, which isn't really enough to carbonate a lager. It's OK for traditional Ales, but for lager you would be better off using bottles.